Suppose there are two types of coins, heads-biased coins and tails-biased coins. A heads-biasedcoin has a 3/4 probability of a heads, while a tails-biased coin has a 1/4 probability of heads. Theproportion of all coins that are heads-biased is 1/7.Suppose that we flip a coin twice and it comes up HH.(a) For a standard Bayesian information processor:(i) What is the person's posterior probability that the coin is heads-biased?(ii) What is the person's forecast for a third flip being H?(b) For an (N = 8)-Freddy (as defined in class):(i) What is the person's posterior probability that the coin is heads-biased?(ii) What is the person's forecast for a third flip being H?(c) Repeat parts (a) and (b) when the proportion of all coins that are heads-biased is 6/7.(d) How do Freddy's forecasts compare to a Bayesian's forecasts? Provide some intuition foryour conclusions.

Answered: that we flip a coin twice and it comes…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 10 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below. Car 1 2 3 4 5 6 7 8 9 10 Brand 1 0.61 0.45 0.46 0.45 0.34 0.43 0.58 0.46 0.62 0.34 Brand 2 0.33 0.37 0.25 0.50 0.30 0.27 0.47 0.32 0.33 0.27 Difference(Brand 1 - Brand 2) 0.28 0.08 0.21 −0.05 0.04 0.16 0.11 0.14…
A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 10 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in Table 1. Car Brand 1 Brand 2 Difference(Brand 1 - Brand 2) 1 0.362 0.293 0.069 2 0.363 0.335 0.028 3 0.220 0.168 0.052 4 0.364 0.297 0.067 5 0.399 0.395 0.004 6 0.351 0.338 0.013 7 0.386 0.377 0.009 8 0.276 0.251 0.025 9 0.206 0.228 -0.022 10 0.340 0.291 0.049 Table 1 Based on these data, can the consumer group conclude, at the 0.10…
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A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 12 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in Table 1. Car Brand 1 Brand 2 Difference(Brand 1 - Brand 2) 1 0.375 0.194 0.181 2 0.238 0.111 0.127 3 0.232 0.265 -0.033 4 0.201 0.184 0.017 5 0.366 0.203 0.163 6 0.206 0.106 0.100 7 0.254 0.311 -0.057 8 0.369 0.242 0.127 9 0.378 0.287 0.091 10 0.349 0.253 0.096 11 0.209 0.235 -0.026 12 0.352 0.188 0.164 Table 1 Based on these data, can the…
A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 12 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below. Car 1 2 3 4 5 6 7 8 9 10 11 12 Brand 1 0.35 0.37 0.51 0.59 0.59 0.42 0.59 0.35 0.38 0.40 0.51 0.34 Brand 2 0.37 0.41 0.49 0.48 0.41 0.21 0.53 0.34 0.34 0.48 0.26 0.19 Difference(Brand 1 - Brand 2) −0.02 −0.04…
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